President Trump and the first lady, Melania Trump, on the South Lawn of the White House last month. The president has vowed to overhaul the nation’s nuclear arsenal.CreditCreditAl Drago/The New York Times

WASHINGTON — When President Barack Obama’s term ended in January, he left a momentous decision to the Trump administration: whether to continue a 30-year, $1 trillion program to remake America’s atomic weapons, as well as its bombers, submarines and land-based missiles.

Mr. Trump has pledged to overhaul the arsenal, which he has called obsolete. But his challenge is growing: The first official government estimate of the project, prepared by the Congressional Budget Office and due to be published in the coming weeks, will put the cost at more than $1.2 trillion — 20 percent more than the figure envisioned by the Obama administration.

The Trump White House’s proposed budget calls for big increases in research and development for new weapons, but it does not yet grapple with the ultimate budget-busting cost of producing a new fleet of delivery vehicles. The Obama administration left the hard budgetary choices for the next administration, and it is unclear whether Mr. Trump’s administration can stomach the rising cost.

“This is why there is no real five-year plan for the defense budget,” said Representative Adam Smith, Democrat of Washington and a member of the House Armed Services Committee, who has asked whether the United States needs all of the 1,550 nuclear weapons it can deploy under a 2010 treaty with Russia. “No one wants to face these numbers.”

The new estimate, which was obtained by The New York Times, offers a hard look at what it would take to remake an aging nuclear weapons complex that is vulnerable to cyberattack. While Mr. Obama once talked about eliminating such weapons over a period of decades, Mr. Trump has a different view. In December, he wrote on Twitter that the United States “must greatly strengthen and expand its nuclear capability.”

The Obama administration program envisioned a nuclear arms buildup unseen since the Reagan administration, with all the resonance of a re-emerging cold war. On the table is the development of a new long-range, nuclear-tipped cruise missile that Mr. Obama’s Defense Department embraced but that some leading nuclear strategists consider unnecessary and potentially destabilizing.

While few question the need for a major update to the nation’s nuclear infrastructure — there are B-52 bombers now being maintained or flown by the grandchildren of their original crew members — the United States is facing a bill so large that the Trump administration has yet to fully figure it into its budget projections.

“It’s a staggering estimate,” said Andrew C. Weber, an assistant defense secretary in the Obama administration and a former director of the Nuclear Weapons Council, an interagency body that oversees the nation’s arsenal.

Mr. Weber said that when he was in the government, he advised against developing the cruise missile because of the cost and because he believed it could fuel a new arms race.

At the heart of the debate is the future of America’s relationship with Russia. With Mr. Trump fighting accusations that his associates might have colluded with Russian officials during the election, administration officials acknowledge that it is almost impossible to imagine a new round of arms control negotiations that might ease the need for a major buildup. The Russians are still building, and the United States has accused Moscow of violating an intermediate-range missile treaty, forcing Washington to develop a response.

But also on the table are other revived nuclear weapons, all under the control of the Energy Department, as well as the really big-ticket military items: a stealthy nuclear bomber to replace the B-52 and B-1 bombers, and a fleet of new, silent submarines. Most controversial are plans to overhaul the oldest and most vulnerable part of the American nuclear complex: the Minuteman missiles that are buried in silos across the Midwest and West. The Pentagon conceded last year that the missiles are so antiquated that they are still run on eight-inch floppy computer disks.

Upgrading the missiles would be among the most expensive parts of a Trump military buildup, and critics say it is time to give them up.

“There are ways to save money for the country that do not in any way put us at risk,” said Tom Z. Collina, director of policy for Ploughshares Fund, an independent organization that favors nuclear arms control, “because many elements of this program are excessive, redundant and dangerous.”

Mr. Collina called the budget office estimate “very credible” and consistent with earlier calculations of the program’s cost.

As Mr. Obama’s initiative becomes Mr. Trump’s, “there is going to be a backlash coming,” particularly among Democrats who had supported the program, said Jon B. Wolfsthal, who oversaw nuclear issues in the Obama White House. He spoke at a May 23 debate on the topic organized by the Center for Strategic and International Studies in Washington.

Other nuclear experts argue that the perils of stopping short of a complete upgrade far outweigh the costs. “This is something that we’ve got to decide it’s time for us to invest, and we’ve got to get moving,” C. Robert Kehler, a retired Air Force general and a former commander of the United States Strategic Command, said at the same event.

A refurbishment of a warhead carried by American bombers, called the B-61, is nearing production, but most of the programs that the Obama administration put in place remain largely in the development phase. The much larger costs of producing the weapons and delivery systems would not come until 2020 or 2021.

The steep rise in costs in the coming years will almost certainly force Congress to choose which programs are the most important for the military, Mr. Weber said. “What’s clear is you save more money by eliminating programs than by buying fewer of something,” he said.

Critics have questioned the need not only for the nuclear-tipped cruise missile, but also for the development of a set of “interoperable warheads” that could be fired from intercontinental ballistic missiles or from submarine-launched missiles. The effective lifetime of those weapons could be extended without producing the interoperable version, the critics say.

Others, like William J. Perry, a defense secretary under President Bill Clinton, have urged a wider redesign of the nuclear deterrent. Mr. Perry has called for eliminating one leg of the “nuclear triad,” which consists of nuclear delivery systems on land, in the air and under the sea. He has argued that the United States would still be safe and save billions of dollars without the intercontinental missiles.

“We simply do not need to rebuild all of the weapons we had during the cold war,” Mr. Perry wrote recently in a Ploughshares publication.

By contrast, Mr. Kehler argued that the triad should be maintained because it posed almost insurmountable problems for any adversary. “In the 21st century, unfortunately, these weapons still exist,” he said, “and, in my humble opinion, are going to exist in the world for as far into the future as we can see.”

A version of this article appears in print on , on Page A16 of the New York edition with the headline: Trump, Who Pledged to Overhaul Nuclear Arsenal, Now Faces Higher Costs. Order Reprints | Today’s Paper | Subscribe